What is the purpose of heap sort?

Heapsort, a renowned sorting algorithm, differs significantly from selection sort in its approach to managing the unsorted region. Rather than engaging in a time-consuming linear scan, heapsort employs a unique strategy.

This strategy revolves around maintaining the unsorted elements in a heap data structure, an efficient method for managing data in a tree-like format. The heap ensures quick access to the largest or smallest element at any given time.

In heapsort, the process begins by transforming the input array into a max-heap, a type of heap where each parent node has a value greater than or equal to its children. This transformation sets the foundation for the sorting operation.

Once the max-heap is established, heapsort iteratively removes the root node (which is the largest element) and places it at the end of the sorted region. To maintain the heap property, the last element of the unsorted region is moved to the root, and the heap is restructured accordingly.

This restructuring process, known as heapify, ensures that the heap's invariant—that the parent node's value is always greater than or equal to its children's—is preserved. By repeatedly performing heapify and swapping, heapsort gradually moves elements from the unsorted to the sorted region.